1. Field of the Invention
This invention relates in general to a method of evaluating silicon wafers and more particularly to a method of evaluating the crystal quality near surface of silicon wafers by means of a microroughness analysis.
2. The Prior Art
A silicon wafer used for manufacturing semiconductor integrated circuits has a device(s) formed on and near surface thereof. The flatness of the surface, an active area of the device(s) is formed thereon, of the silicon wafer is crucial in both macroscopic and microscopic levels. As unevenness at the atomic level, called microroughness, is believed to be reflected by the crystal quality, this microroughness has been evaluated using various techniques.
The microroughness of a silicon wafer surface gets worse after the treatment with a cleaning solution composed of aqueous solution of ammonium hydroxide (NH.sub.4 OH) and hydrogen peroxide (H.sub.2 O.sub.2). Such change of the microroughness after the treatment with a cleaning solution having a relatively weak etching effect on silicon wafers is believed to be reflected by the crystal quality.
However, this etching effect of the cleaning solution is so weak that a technique to detect the microroughness with high sensitivity is required. Moreover, a technique with capability to measure the order of atomic level is required.
An atomic force microscope (hereafter referred to as "AFM") and a scanning tunnelling microscope (hereafter referred to as "STM") are used in techniques for the measurement of the microroughness of silicon wafers in the order of atomic level. An AFM detects the microscopic forces between atoms and a probe, typically van der Waals forces, and detects changes in such forces due to minute differences in the distances between atoms and the probe to determine the surface unevenness.
Since an AFM is capable of very accurately measuring unevenness without destruction of the surface of the specimen, it is ideal for measuring the microroughness. The microroughness obtained by AFM is usually represented by RMS (root mean square), P-V (peak to valley) and so on. Assuming x.sub.i (i=1, 2, . . . , N) to be the height of one of N measurement points from the reference plane, RMS is expressed by the following equation: ##EQU3## Where x denotes: ##EQU4##
P-V is expressed by the following equation: EQU P-V=[x.sub.i ].sub.max -[x.sub.i ].sub.min
Where [x.sub.i ].sub.max is the maximum of x.sub.i and [x.sub.i ].sub.min is the minimum of X.sub.i.
As a prior art for the microroughness change evaluation of silicon wafers after the treatment with a cleaning solution having a composition of NH.sub.4 OH/H.sub.2 O.sub.2 /H.sub.2 O=1:1:5, T. Ohmi et al. reported the relationship between the microroughness and the crystal quality of various samples including Czochralski grown crystals, float zoned crystals and epitaxial grown crystals using average roughness (Ra).
Here, Ra is a microroughness evaluation similar to RMS, as shown in the following equation: ##EQU5## Where x denotes: ##EQU6##
The evaluation method described above takes measurements in a scanning area of a prescribed size at several points. RMS value is shown to change differently depending on the types of silicon crystals when the microroughness measurements are carried out on a silicon wafer using different sizes of scanning area.
FIG. 3 shows the relationship between the size of the scanning area (horizontal axis) and RMS (vertical axis) in the evaluation method described above. In this figure, the samples represented by circles have a haze level of 7 (BIT) without a heat treatment, the samples represented by squares have a haze level of 16 (BIT) with 20 minutes of a heat treatment at 1000.degree. C., and the samples represented by triangles have a haze level of 107 (BIT) with several hours of a heat treatment at 1100.degree. C. "Haze level" is an indicator of the microroughness obtained by an optical method, and a larger haze level values indicates more rough surface. As shown in the figure, the RMS value changes depending on the size of the scanning area and a good correlation with the haze level cannot be obtained.
The evaluation method described above has to be a microroughness evaluation based on RMS or Ra using a certain fixed size of the scanning area. However, such a RMS microroughness evaluation with a fixed size of the scanning area is not an appropriate evaluation of the crystal quality because it is not comprehensive. That is, because the scanning area of the AFM measurement is very small, it is difficult to grasp the silicon surface configuration with a calculation method such as RMS.
On the other hand, the microroughness of a silicon wafer surface affects the dielectric breakdown properties of an oxide layer. However, the evaluation of dielectric breakdown properties with a fabricating MOS structure on a silicon wafer surface requires complicated and time consuming process such as oxidation or formation of electrodes.